Scattering theory of molecules, atoms and nuclei:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Singapore [u.a.]
World Scientific
2013
|
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025756952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 613 - 623 |
| Umfang: | XVI, 629 S. graf. Darst. |
| ISBN: | 9789814329835 |
Internformat
MARC
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| 020 | |a 9789814329835 |9 978-981-432983-5 | ||
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| 100 | 1 | |a Canto, Luiz Felipe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Scattering theory of molecules, atoms and nuclei |c Luiz Felipe Canto ; Mahir S. Hussein |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 2013 | |
| 300 | |a XVI, 629 S. |b graf. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 613 - 623 | ||
| 700 | 1 | |a Hussein, Mahir S. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025756952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025756952 | |
Datensatz im Suchindex
| _version_ | 1819338431657934848 |
|---|---|
| adam_text | Titel: Scattering theory of molecules, atoms and nuclei
Autor: Canto, Luiz Felipe
Jahr: 2013
Contents
Preface vii
Acknowledgments ix
Part 1: Potential Scattering 1
1. Basic Notions 3
1.1 Introduction.......................... 3
1.2 Several definitions ...................... 5
1.2.1 Types of collisions - reaction Channels...... 6
1.2.2 Q-values, threshold, open and closed Channels . . 7
1.3 Cross sections......................... 8
1.3.1 Center of mass and Iaboratory frames....... 9
1.4 Classical scattering...................... 14
1.4.1 The classical cross section ............. 16
1.4.2 Orbiting, rainbow and glory scattering...... 18
1.5 Stationary scattering of a plane wave............ 22
1.6 Scattering of a wave packet................. 25
1.6.1 Propagation of a free wave packet......... 25
1.6.2 Collision of the wave packet with a target..... 29
1.6.3 The Optica! Theorem................ 33
1.7 Systems of units....................... 36
1.7.1 Nuclear physics................... 36
1.7.2 Atomic and molecular physics........... 38
XI
xii Scattering Theory of Molecules, Atoms and Nuclei
2. The Partial Wave Expansion Method 41
2.1 Free particle in spherical coordinates............ 44
2.2 Numerical Solutions of the radial equation......... 47
2.3 Scattering amplitude and cross section........... 50
2.4 Wronskian relations ..................... 55
2.5 Integral formulae for the phase shifts............ 56
2.6 Convergence of the partial-wave expansion......... 57
2.7 Hard sphere scattering.................... 58
2.8 Absolute phase shifts - Levinson Theorem........ 59
2.9 Resonances.......................... 63
2.9.1 Time delay...................... 65
2.10 Scattering from a square-well................ 68
2.11 Low energy scattering.................... 70
2.11.1 The scattering length................ 70
2.11.2 The effective ränge formula............. 73
3. Coulomb Scattering 79
3.1 Classical mechanics description of Coulomb scattering . . 79
3.2 Quantum mechanical description.............. 81
3.2.1 The quantum mechanical cross section in Coulomb
scattering....................... 84
3.3 Partial wave expansion.................... 86
3.3.1 Approximate Coulomb phase shifts - asymptotic
series......................... 88
3.3.2 Some numerical results............... 94
3.3.3 Partial-wave expansion of ^ c+) (k; r)........ 97
3.4 Coulomb plus short-range potentials............ 98
3.4.1 An illustration: a - a scattering.......... 102
4. Green s Functions, T- and S-Matrices 107
4.1 Lippmann-Schwinger equations............... 107
4.1.1 The free particle Green s function......... 109
4.1.2 The scattering amplitude.............. 113
4.1.3 Orthonormahty relation for scattering states . . . 115
4.1.4 The M0ller wave Operators............. 116
4.2 The transition and the scattering Operators........ 117
4.2.1 The Optica! Theorem................ 119
4.2.2 The S-matrix .................... 120
Contents xiii
4.3 The time-dependent picture................. 122
4.3.1 Time-dependent definition of the scattering
Operator ....................... 125
4.3.2 Energy conservation................. 127
4.3.3 Time-reversal .................... 128
4.4 Scattering from non-local separable potentials....... 130
4.5 Scattering from the sum of two potentials......... 133
4.5.1 The Gell-Mann Goldberger relations........ 134
4.5.2 The Distorted Wave series............. 135
4.6 Partial-wave expansions................... 136
4.6.1 Partial-wave projection of the S- and the
T-matrices...................... 139
4.6.2 The partial-wave projected two-potential formula 142
4.7 Long ränge potentials .................... 142
4.8 Evaluation of partial-wave Green s functions........ 146
4.8.1 Free particle s Green s function .......... 147
4.8.2 Green s functions for an arbitrary potential .... 150
5. Approximate Methods in Potential Scattering 157
5.1 Perturbative approximations ................ 157
5.1.1 The Born series................... 157
5.1.2 The Distorted Wave Born series.......... 166
5.2 Semiclassical approximations................ 177
5.2.1 The eikonal approximation............. 177
5.2.2 The WKB approximation.............. 190
5.2.3 The semiclassical scattering amplitude ...... 211
6. Spin and Identical Particles 247
6.1 Collisions of particles with spin............... 247
6.1.1 Partial-wave expansions............... 250
6.2 The scattering of a spin ^2 particle............. 262
6.2.1 The eikonal approximation in collisions of a
spin- ^2 particle................... 269
6.3 Identical particles....................... 273
6.3.1 Collisions of identical spinless particles and
particles with aligned spins............. 275
6.3.2 Collisions of identical particles with spin..... 280
6.3.3 Clusters of identical fermions............ 284
xiv Scattering Theory of Molecules, Atoms and Nuclei
7. Scattering from Complex Potentials 291
7.1 The absorption cross section................. 291
7.2 Lippmann-Schwinger equations with complex potentials . 296
7.3 The scattering and the transition Operators........ 301
7.3.1 Low s equation and the generalized Optical
Theorem....................... 303
7.4 Partial-wave expansions................... 305
7.5 Diffractive scattering..................... 307
7.5.1 Fraunhofer diffraction................ 308
7.5.2 Fresnel diffraction.................. 315
7.6 Realistic treatments of elastic scattering with absorptive
potentials........................... 323
8. Additional Topics 341
8.1 Analytical properties of the S-matrix............ 341
8.1.1 The Jost function.................. 341
8.1.2 Analytical continuation in the complex k- and
^-planes....................... 343
8.1.3 Bound states..................... 346
8.1.4 Resonances...................... 350
8.1.5 Analytical continuation into the complex /-plane . 353
8.2 Quantum scattering in 1D and 2D............. 355
8.2.1 Brief account of quantum scattering in 1D .... 356
8.2.2 Brief account of quantum scattering in 2D .... 360
8.2.3 Semiclassical scattering in 2D ........... 368
8.3 The inverse scattering problem............... 373
8.4 The Calogero equation for neutral particle scattering . . . 377
8.4.1 The Calogero equation for charged particle
scattering....................... 380
Part 2: Many-body Scattering 383
9. The Coupled Channel Formalism 385
9.1 The close coupling approximation.............. 388
9.1.1 Absorption in multi-channel scattering...... 391
9.2 The Lippmann-Schwinger equations ............ 393
9.2.1 M0ller Operators, the T- and the S-matrices . . . 397
Contents xv
9.3 Partial-wave expansions................... 399
9.3.1 Collisions of spinless particles ........... 399
9.3.2 Partial-wave expansions with spin......... 409
9.3.3 Evaluation of matrix-elements........... 419
9.4 Coupling with continuum states............... 424
9.5 Solution of the coupled Channel equations......... 431
10. Few-channel Description of Many-body Scattering 441
10.1 The Feshbach calculus.................... 442
10.1.1 The dispersion relation for Heff .......... 445
10.2 Prompt processes, time delay and resonances....... 446
10.2.1 Prompt processes: direct reactions......... 447
10.2.2 Long-lived resonances................ 448
10.3 Energy averages and the optical model........... 459
10.4 Optical potentials....................... 464
10.4.1 Optical potentials in nucleon-nucleus collisions . . 465
10.4.2 Optical potentials in nucleus-nucleus collisions . . 473
10.5 Dynamic polarization potentials............... 487
10.5.1 Adiabatic polarization potentials.......... 490
10.5.2 Polarization potentials in the sudden limit .... 498
10.5.3 Realistic polarization potentials.......... 507
10.5.4 Threshold anomaly................. 509
10.6 Scattering from energy-dependent potentials........ 512
11. Approximate Methods in Many-body Scattering 517
11.1 Perturbative approximations ................ 518
11.1.1 The Plane Waves Born Approximation...... 519
11.1.2 The Distorted Waves Born Approximation .... 521
11.1.3 The Coupled Channel Born Approximation .... 523
11.2 Semiclassical approximations ................ 524
11.2.1 The classical trajectory approximation...... 524
11.2.2 The classical-limit S-matrix............. 538
11.2.3 Glauber approximation............... 545
12. Selected Topics in Many-body Scattering 551
12.1 Doorway resonances..................... 551
12.2 Feshbach resonances in atom-atom collisions........ 563
xvi Scattering Theory of Molecules, Atoms and Nuclei
12.3 Statistical treatment of complex scattering: the
Compound nucleus...................... 568
12.3.1 Fluctuation cross section.............. 576
12.3.2 Fluctuation part of angular distributions..... 581
12.4 Chaotic scattering...................... 585
12.4.1 Ericson fluctuations................. 585
12.4.2 Hanbury Brown-Twiss correlations ........ 588
12.5 Scattering in media and nuclear astrophysics ....... 593
12.6 Multiple scattering...................... 600
12.7 The three-body problem and Faddeev equations...... 603
12.8 The R-matrix method.................... 606
12.8.1 The calculable R-matrix .............. 607
12.8.2 The phenomenological R-matrix.......... 611
Bibliograph]) 613
Index 625
|
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| id | DE-604.BV040778671 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:25:32Z |
| institution | BVB |
| isbn | 9789814329835 |
| language | English |
| lccn | 2012046470 |
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| physical | XVI, 629 S. graf. Darst. |
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| publisher | World Scientific |
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| spellingShingle | Canto, Luiz Felipe Hussein, Mahir S. Scattering theory of molecules, atoms and nuclei |
| title | Scattering theory of molecules, atoms and nuclei |
| title_auth | Scattering theory of molecules, atoms and nuclei |
| title_exact_search | Scattering theory of molecules, atoms and nuclei |
| title_full | Scattering theory of molecules, atoms and nuclei Luiz Felipe Canto ; Mahir S. Hussein |
| title_fullStr | Scattering theory of molecules, atoms and nuclei Luiz Felipe Canto ; Mahir S. Hussein |
| title_full_unstemmed | Scattering theory of molecules, atoms and nuclei Luiz Felipe Canto ; Mahir S. Hussein |
| title_short | Scattering theory of molecules, atoms and nuclei |
| title_sort | scattering theory of molecules atoms and nuclei |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025756952&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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